Multiple players ruin problems and the Dirichlet heat kernel in compact inner-uniform domains
We describe detailed two-sided inequalities for the three-player ruin problem and related estimates for killed random walks in inner-uniform finite subset of grids and other graphs. The key is the simultaneous use of the appropriate Doob transform, doubling and Poincaré inequalities. This talk is based on joint work with Persi Diaconis and Kelsey Houston-Edwards.